Related papers: Measurable Cones and Stable, Measurable Functions
Building and expanding on principles of statistics, machine learning, and scientific inquiry, we propose the predictability, computability, and stability (PCS) framework for veridical data science. Our framework, comprised of both a…
We define Conditional quasi concave Performance Measures (CPMs), on random variables bounded from below, to accommodate for additional information. Our notion encompasses a wide variety of cases, from conditional expected utility and…
This paper concerns algorithms that give correct answers with (asymptotic) density $1$. A dense description of a function $g : \omega \to \omega$ is a partial function $f$ on $\omega$ such that $\left\{n : f(n) = g(n)\right\}$ has density…
The existence, uniqueness, and asymptotic stability of modulo periodic Poisson stable solutions of dynamic equations on a periodic time scale are investigated. The model under investigation involves a term which is constructed via a Poisson…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
In this paper, the notion of $\mathbb{C}$-simulation function is introduced and the existence and uniqueness of common fixed points of two self-mappings satisfying contractive conditions in the setting of complex valued metric spaces via…
We introduce the {\em $\mu$-topological stability}. This is a type of stability depending on the measure $\mu$ different from the set-valued approach \cite{lm}. We prove that the map $f$ is $m_p$-topologically stable if and only if $p$ is a…
In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.
We consider the problem of characterizing entrywise functions that preserve the cone of positive definite matrices when applied to every off-diagonal element. Our results extend theorems of Schoenberg [Duke Math. J. 9], Rudin [Duke Math. J.…
Given an infinitesimal perturbation of a discrete-time finite Markov chain, we seek the states that are stable despite the perturbation, \textit{i.e.} the states whose weights in the stationary distributions can be bounded away from $0$ as…
We exhibit a functor from the category OUS of order unit spaces and positive, unit-preserving mappings into the category $\Prob$ of probabilistic models (test spaces with designated state spaces) and morphisms thereof. Restricted to any…
Given a closed, convex cone $K\subseteq \mathbb{R}^n$, a multivariate polynomial $f\in\mathbb{C}[\mathbf{z}]$ is called $K$-stable if the imaginary parts of its roots are not contained in the relative interior of $K$. If $K$ is the…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…
We study the stability of linear fractional order maps. We show that in the stable region, the evolution is described by Mittag-Leffler functions and a well defined effective Lyapunov exponent can be obtained in these cases. For…
In this brief note, we investigate some constructions of Lyapunov functions for stochastic discrete-time stabilizable dynamical systems, in other words, controlled Markov chains. The main question here is whether a Lyapunov function in some…
We prove a theorem which provides a method for constructing points on varieties defined by certain smooth functions. We require that the functions are definable in a definably complete expansion of a real closed field and are locally…
We define two equivalent notions of twisted stable map from a curve to a Deligne-Mumford stack with projective moduli space, and we prove that twisted stable maps of fixed degree form a complete Deligne-Mumford stack with projective moduli…
We extend and improve the existing characterization of the dynamics of general quadratic real polynomial maps with coefficients that depend on a single parameter $\lambda$, and generalize this characterization to cubic real polynomial maps,…